Integral Help

I have an integral in a physics problem that I can't solve. How would I go about solving the following:
[tex]\int e^{a\left[\left(\frac{x}{b}\right)^{\frac{1}{4}}-1\right]}dx[/tex]
where a and b are constants

You can make it look slightly less intimidating:
[tex]\int e^{a\left[\left(\frac{x}{b}\right)^{\frac{1}{4}}-1\right]}dx\,=\,e^{-a}\int e^{a\left(\frac{x}{b}\right)^{\frac{1}{4}}\,=\,\LARGE e^{-a}\int e^{cx^{\frac{1}{4}}}\,,[/tex]
where c = a/b^1/4.